Allegedly, Beethoven condensed Fux's work into a "cheat sheet" version for ready reference (from the back cover of the Alfred Mann translation), and Mozart apparently annotated his own copy (according to Wikipedia). I feel like it would be so cool to see these primary source materials, but i'm not sure if they have been preserved in any fashion. Does anyone have any information here?
Thanks!
Okay, there's a lot of confusing information out there about what materials exist related to Fux's Gradus ad Parnassum and their connection to significant composers.
But let's start with Beethoven. His summary of Fuxian counterpoint wasn't exactly something he prepared for "ready reference." Beethoven had avoided teaching composition a number of times, but finally in 1809 he was met with a situation where he couldn't really refuse a pupil -- Archduke Rudolph. Beethoven needed to prepare some pedagogical materials. Among those, for the teaching of counterpoint, he chose a number of excerpts and musical examples from Fux (and some other treatises), which he collected and annotated.
This resulted in Beethoven's Einleitung zur Fuxischen Lehre vom Kontrapunkt, apparently a 73-page document (on 37? leaves). Nottebohm (one of Beethoven's early biographers) published a summary in Beethoveniana in 1872, which can be found here (starting on page 177). (If that direct link doesn't work, you can get to the document from this page.) That summary, which gives the beginning of each topic and a list of most of the musical excerpts from Fux that Beethoven apparently had collected from the German edition of the Gradus, is the only published one that modern scholarly indexes seem to list. I was able to find what seems to be an actual transcription of maybe the first half or so that was published by Nottebohm in the Allgemeine musicalische Zeitung (No. 46, 11 Nov 1863), which can be found online here beginning on page 770. I have no idea why modern scholars seemingly have forgotten about this version in the AMZ, but it's pretty useful. Unfortunately, I haven't seen a reference to any complete edition or any modern edition. (EDIT: I realized there is a continuation of Nottebohm's transcription beginning on page 784 of that linked AMZ volume. I don't know whether all of this contains the complete text and examples of the Fux section or not.) What seems to be the last manuscript page of this document is available digitally from the Beethoven-Haus archive website here (though you'll have to be able to read through Beethoven's altdeutsche Schrift scrawl to sort out what it says). The rest of the manuscript is apparently still in the possession of the Gesellschaft der Musikfreunde archive in Vienna. Unfortunately, their online catalog is a bit wonky, and I don't know if they've digitized much of anything.
(Important note: whatever you do, don't believe what you find in Seyfried's book about Beethoven's compositional instruction. Seyfried was a fellow student with Beethoven under Albrechtsberger and originally came into possession of Beethoven's teachings on counterpoint and other things after Beethoven's death. He published a version in German that claimed to be Beethoven's work, and it was ultimately translated into French and even English, where it was published by Pierson in 1853. (Copy available here.) Seyfried made the following claim in his introduction: "These studies of the unforgettable master represent so invaluable a legacy to the entire world of the arts that it would have been preposterous to make even the slightest changes." Don't believe a word of it. As Nottebohm later wrote, Seyfried's "edition" of Beethoven's studies was "neither authentic nor fictitious but forged." There is some of Beethoven in there, but it's in no way an accurate rendition of anything Beethoven wrote. Some people have apparently taken to reissuing this Pierson book in recent years, as it's free and easy to make copies, but don't take it to be Beethoven's work.)
Anyhow, the archive of the Gesellschaft der Musikfreunde also is in possession of Beethoven's studies of Fux with Haydn (54 pages), as discussed in Alfred Mann's article "Beethoven's Contrapuntal Studies with Haydn." These too have not been published in any modern edition, but they contain Beethoven's exercises with Haydn's corrections, as Mann discusses.
While we're on the subject of Haydn, even though the question didn't specifically ask about him, Haydn did prepare a summary of contrapuntal rules largely derived from Fux, in what is known as Haydn's Elementarbuch. Again, to my knowledge, this has not been published in any edition, but there's a decent discussion of it in Alfred Mann, "Haydn's Elementarbuch: A document of classic counterpoint instruction," in Salzer and Mitchell, eds., The Music Forum Vol. 3 (1973). (This book is available in larger libraries; it's part of a pretty classic series of American music theory books.)
Haydn's own copy of Fux's Gradus was apparently heavily annotated. It was destroyed in World War II, but the annotations had (luckily!) been previously copied by Carl Ferdinand Pohl onto another copy of Fux's treatise, which is also in that magical Viennese archive I've mentioned above. Again, I'm not aware of any published edition.
On to Mozart...
Don't believe anything you read in Wikipedia unless you verify it. (Seriously, the music history articles are riddled with errors and scholarship that's 50 years out of date.) If you follow the supposed citation in Fux's Wikipedia article for the sentence: "Mozart had a copy of it that he annotated," it takes you to this Britannica article, which makes no such claim. (Hint: if you're a Wikipedia editor who wants to put false information in Wikipedia, put in a citation that looks like it should contain the information but doesn't. Very few people check this stuff.) The Britannica article only mentions that Fux "was studied by Wolfgang A. Mozart, Joseph Haydn, and other 18th-century composers."
Anyway, what I assume this misguided Wikipedia editor was on about was actually regarding the wrong Mozart. Wolfgang did possess a copy of Fux (in the original Latin), which he got from his father's library. Leopold Mozart did have that copy and apparently used it in his teaching (likely of his son). Many people have claimed that this copy was "annotated" (including Mann, in his introduction to the Fux translation that was discussed in the question), but apparently Mann never bothered to take a trip to the Mozarteum in Salzburg and actually look at the book. Luckily, it has now been digitized and is available online here. I skimmed through the roughly 300 pages and didn't see any annotations aside from the stuff at the beginning that it came from Leopold's library. Maybe there are some annotations in there, but if so, they're pretty sparse.
So, not only does Wikipedia get it wrong, so did Alfred Mann. Oh well. No annotations from the Mozart family that I could find.
Still, we have something that's a little more fun and useful from Mozart, namely his studies on Fuxian counterpoint with his student Thomas Attwood, available in Series X (Volume 30, No. 1) of the Neue Mozart-Ausgabe. (I don't think I can direct-link volumes of the NMA, but you can start at the homepage and navigate to the appropriate volume (number 114).) Mozart clearly used and knew Fux extensively. His corrections of Attwood's exercises and occasional rewriting of some excerpts is interesting. I haven't gone back through this now, but my favorite part I recall is when Attwood messed up some clefs somewhere or something, and Mozart just put big X's over the whole thing and wrote "You are an ass" repeatedly. (Mozart usually seemed to write feedback to Attwood in Italian, but could use some of his limited English when he was a bit feisty... I think Mozart could swear well in a half-dozen languages, but that's a different issue.)
In any case, the general situation is -- yes, famous Viennese composers liked and used Fux, and they left behind quite a few documents related to the use of the Gradus in pedagogy. Unfortunately, little of this has been digitized or published, and almost none of it is in English (if that's an issue), aside from Mozart's occasional annoyed comments to his English-speaking student.
